This section provides background information related to the present disclosure which is not necessarily prior art. One of the hallmarks of turbulence is the formation of rotating currents known as vortices. Measuring the vorticity, the average angular velocity exhibited by molecules in a small cylindrical volume in space, is of great importance in fluid dynamics, especially for aerodynamic design and control of air flight. Vorticity gives the local rate of rotation of a fluid element. It plays a pivotal role in the fundamental description and understanding of fluid dynamics. Vorticity caused by airplanes increases drag and therefore results in billions of dollars in increased fuel costs and the associated use of nonrenewable resources and increased carbon footprint. Vorticity results from gradients in fluid dynamics, and is closely associated with turbulence.
Direct experimental data in thin turbulent boundary layers are difficult to obtain, and often the only source of information comes from complex computer models that have to run on supercomputers. The complexity of this problem was noted in the 1970s by Richard Feynman, who stated “Turbulence is the most important unsolved problem of classical physics”. Although computer models are yielding valuable insight into the complex physics of wall-bounded turbulence, a method capable of obtaining experimental measurements of the turbulence and emergence of vorticity at a shear boundary layer would be of tremendous value for fluid dynamics, especially if results can be obtained in real time and not require months of computer time.
Vorticity is mathematically defined as the curl of the velocity vector, Ω=∇×U, and is physically interpreted as twice the local rotation rate (angular velocity) ω of a fluid particle, i.e. Ω=2ω. It is one of the most dynamically important flow variables and is fundamental to the basic flow physics of many areas of fluid dynamics, including aerodynamics, turbulent flows and chaotic motion. In a turbulent flow, unsteady vortices of various scales and strengths contribute to the chaotic nature of turbulence. Even though spatially- and temporally-resolved direct measurement of instantaneous vorticity has been a long-held goal, it has proven elusive to date.
The first direct measurement of vorticity was attempted more than three decades ago by measuring the rotation rate of planar mirrors embedded in 25 μm transparent spherical beads that were suspended in a refractive-index-matched liquid. This method has rarely been utilized since the implementation of the method is very complex and the requirement of index matching significantly limits its use and prohibits its application in gas (air) flows.
Currently in all non-intrusive methods, whether particle-based, such as Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV), or molecular-based, as in Molecular Tagging Velocimetry (MTV), vorticity is estimated from a number of velocity field measurements at several points near the point of interest, which then allow computation of the velocity derivatives over space. These methods provide a measurement of vorticity that is spatially averaged over the (small) spatial resolution area of each method.
Presently, experimental vortex characterization involves acquiring multiple measurements, from which the fluid velocity vectors are determined in space and used to calculate vorticity through vector (cross) product. Velocity field of a fluid flow can be obtained by analyzing images of scattered laser light with particle image velocimetry or images of phosphorescence of laser excited molecules in molecular tagging velocimetry. Fluid dynamics would be greatly enhanced if a method for vortex characterization could be developed that bypassed the determination of the velocity vector field in space but had the capability of directly determining the magnitude and sign of vorticity at a point in space.